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Chapter 8: Q. 41 (page 497)

A TV poll A television news program conducts a call-in poll about a proposed city ban on handgun ownership. Of the 2372 calls, 1921 oppose the ban. The station, following recommended practice, makes a confidence statement: "81%of the Channel 13 Pulse Poll sample opposed the ban. We can be 95% confident that the true proportion of citizens opposing a handgun ban is within1.6% of the sample result."

(a) Is the station's quoted 1.6% margin of error correct? Explain.

(b) Is the station's conclusion justifed? Explain.

Short Answer

Expert verified

a) No

b) No

Step by step solution

01

Part (a) Step1 : Given Information

Need to explain the margin of error quoted is1.6%

02

Part (a) Step2: Explanation

No, because the sample is a voluntary response sample, the confidence interval method's randomness condition is not met, and so the claimed1.6 percent margin of error is wrong.

03

Part (b) Step 2: Given Information 

Need to explain the stations conclusion.

04

Explanation(Part b)

No, because the sample is a voluntary response sample, the confidence interval method's randomization condition is not met, and hence the conclusion based on the confidence interval is erroneous.

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Most popular questions from this chapter

It's about ME Explain how each of the following would affect the margin of error of a confidence interval, if all other things remained the same.

(a) Increasing the confidence level

(b) Quadrupling the sample size

Good wood? A lab supply company sells pieces of Douglas fir 4inches long and 1.5inches square for force experiments in science classes. From experience, the strength of these pieces of wood follows a Normal distribution with standard deviation 3000pounds. You want to estimate the mean load needed to pull apart these pieces of wood to within 1000pounds with 95%confidence. How large a sample is needed? Show your work.

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Equality for women? Have efforts to promote equality for women gone far enough in the United States? A poll on this issue by the cable network MSNBC contacted 1019adults. A newspaper article about the poll said, “Results have a margin of sampling error of plus or minus 3 percentage points.”15

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